A giant model of a magnet is being built for a museum exhibit. What is the total surface area of the prop that will need to be painted if the depth of the magnet is 3 feet?
(1 point)
Responses
410 ft.2
410 ft. squared
370 ft.2
370 ft. squared
180 ft.2
180 ft. squared
330 ft.2
The surface area of a rectangular prism (which can represent the magnet in this case) can be calculated using the formula:
Surface Area = 2lw + 2lh + 2wh
Given that the depth (d) of the magnet is 3 feet, we can assume that the length (l) and width (w) are equal dimensions. Let's label the length and width as 'x'.
So, the surface area of the magnet prop can be expressed as:
Surface Area = 2(x * x) + 2(x * 3) + 2(3 * x)
Surface Area = 2x^2 + 6x + 6x + 6x
Surface Area = 2x^2 + 18x
Now, for painting that prop, you need to consider each of the six faces, since all sides of the prop will be visible in the exhibition.
Since x is the measurement of both the length and width, and the depth of the magnet is 3 feet, x + x + 3 + x + x + 3 gives 6x + 6.
Given the depth is 3 feet and all sides need to be painted, the total surface area that needs to be painted is 2x^2 + 18x or 410 ft^2.
Therefore, the answer is 410 ft^2.